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Theorems · Theorem · group theory

DivisibleBy.surjective_smul

∀ (A : Type u_1) (α : Type u_2) [inst : AddMonoid A] [inst_1 : SMul α A] [inst_2 : Zero α] [DivisibleBy A α] {n : α},
  n ≠ 0 → Function.Surjective fun a => n • a
Defined in
Mathlib.GroupTheory.Divisible
Cited by
2 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
AddMonoidSMulZeroDivisibleBy
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Measure.measurePreserving_zsmul · cited by 2Measure.measurePreserving…smul_right_surj_of_divisibleBy · cited by 0smul_right_surj_of_divisi…AddMonoid · cited by 2864AddMonoidDivisibleBy · cited by 8DivisibleByDivisibleBy.div · cited by 6DivisibleBy.divDivisibleBy.div_cancel · cited by 4DivisibleBy.div_cancelDivisibleBy.surjective_smulCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.